I love working out and I love running. I do 5Ks now, but would love to train for a marathon. However, I get such terrible anxiety when I work out that I have to stop. Even when I know I haven't pushed myself nearly hard enough to get ill, I still panic.
I was in track in high school and I never saw anybody actually get sick from it. You know your body and you know your limits, so trust yourself. You should never want to push yourself so hard you actually throw up. You will know when you need to stop.
But in general, stay hydrated and don't gulp or drink ice cold water. That can upset your stomach during a workout. Also I was told never to bend over to catch your breath, but to squat down. I guess the bending over can make your stomach think it's over full when you're taking the deep breaths. Not sure how true it is, but I do it anyway.